In an interview with CNN, Senate Majority Leader Mitch McConnell would not say if the GOP conference would welcome him into its weekly policy lunches or give him committee assignments.
"That's a good conversation for sometime after tomorrow," McConnell said in the Capitol.
Other top Republicans also punted when asked whether Moore would be named to any committee -- a remarkably unusual move given that most senators tend to serve on four to five panels each.
"None of that has been discussed or decided," said Senate Majority Whip John Cornyn of Texas.
Being denied a committee assignment could significantly undercut Moore's ability to be effective in the Senate. It would deny him the ability to work on legislation and attend hearings with witnesses about policy matters, alienating him in a body that already has revolted from him in the aftermath of allegations of sexual misconduct, including with minors.
Behind the scenes, GOP senators have been discussing their options on how to handle Moore, and the consensus is to pursue the matter with the Senate Ethics Committee, which could recommend his expulsion to the full Senate.
But an ethics investigation could take months, leaving Moore in limbo in the Senate -- especially if he's denied committee assignments.
Sen. Richard Shelby, the senior Alabama GOP senator who opposes Moore's candidacy,
refused to say if he supports seating the candidate on a committee.
"That's up to the leadership," Moore said. "You need to talk to McConnell."
Don Stewart, a McConnell spokesman, said the issue will be settled by the 52-member conference, not the GOP leader alone.
"I'm sure the conference will have plenty of discussions on the issue," Stewart said.
Yet, roughly a dozen Senate Republicans on Monday night would not say whether they supported seating him on a committee.
"There are a lot of unanswered questions, and we will see what happens in the election," said Sen. Shelley Moore Capito of West Virginia.